國立虎尾科技大學 |

Introduction to the Representation Theory of Algebras

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Introduction to the Representation Theory of Algebras/ by Michael Barot.
作者:	Barot, Michael.
面頁冊數:	X, 179 p. 109 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Associative rings. -
電子資源:	https://doi.org/10.1007/978-3-319-11475-0
ISBN:	9783319114750

Introduction to the Representation Theory of Algebras
Barot, Michael.

Introduction to the Representation Theory of Algebras[electronic resource] /by Michael Barot. - 1st ed. 2015. - X, 179 p. 109 illus.online resource.

Matrix Problems -- Representations of Quivers -- Algebras -- Module Categories -- Elements of Homological Algebra -- The Auslander-Reiten Theory -- Knitting -- Combinatorial Invariants -- Indecomposables and Dimensions.

This book gives a general introduction to the theory of representations of algebras. It starts with examples of classification problems of matrices under linear transformations and explains the three common setups: representation of quivers, modules over algebras and additive functors over certain categories. The main part is devoted to (i) module categories, presenting the unicity of the decomposition into indecomposable modules, the Auslander–Reiten theory and the technique of knitting; (ii) the use of combinatorial tools such as dimension vectors and integral quadratic forms; and (iii) deeper theorems such as Gabriel‘s Theorem, the trichotomy and the Theorem of Kac – all accompanied by further examples. Each section includes exercises to facilitate understanding. By keeping the proofs as basic and comprehensible as possible and introducing the three languages at the beginning, this book is suitable for readers from the advanced undergraduate level onwards and enables them to consult related, specific research articles.

ISBN: 9783319114750

Standard No.: 10.1007/978-3-319-11475-0doiSubjects--Topical Terms:

893564
Associative rings.

LC Class. No.: QA251.5

Dewey Class. No.: 512.46

Introduction to the Representation Theory of Algebras
LDR:02552nam a22003855i 4500 001 970728
003 DE-He213
005 20200701101138.0
007 cr nn 008mamaa
008 201211s2015 gw | s |||| 0|eng d
020 $a 9783319114750 $9 978-3-319-11475-0
024 7 $a 10.1007/978-3-319-11475-0 $2 doi
035 $a 978-3-319-11475-0
050 4 $a QA251.5
072 7 $a PBF $2 bicssc
072 7 $a MAT002010 $2 bisacsh
072 7 $a PBF $2 thema
082 0 4 $a 512.46 $2 23
100 1 $a Barot, Michael. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1065265
245 1 0 $a Introduction to the Representation Theory of Algebras $h [electronic resource] / $c by Michael Barot.
250 $a 1st ed. 2015.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a X, 179 p. 109 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
505 0 $a Matrix Problems -- Representations of Quivers -- Algebras -- Module Categories -- Elements of Homological Algebra -- The Auslander-Reiten Theory -- Knitting -- Combinatorial Invariants -- Indecomposables and Dimensions.
520 $a This book gives a general introduction to the theory of representations of algebras. It starts with examples of classification problems of matrices under linear transformations and explains the three common setups: representation of quivers, modules over algebras and additive functors over certain categories. The main part is devoted to (i) module categories, presenting the unicity of the decomposition into indecomposable modules, the Auslander–Reiten theory and the technique of knitting; (ii) the use of combinatorial tools such as dimension vectors and integral quadratic forms; and (iii) deeper theorems such as Gabriel‘s Theorem, the trichotomy and the Theorem of Kac – all accompanied by further examples. Each section includes exercises to facilitate understanding. By keeping the proofs as basic and comprehensible as possible and introducing the three languages at the beginning, this book is suitable for readers from the advanced undergraduate level onwards and enables them to consult related, specific research articles.
650 0 $a Associative rings. $3 893564
650 0 $a Rings (Algebra). $3 685051
650 0 $a Category theory (Mathematics). $3 1255325
650 0 $a Homological algebra. $3 1255326
650 0 $a Algebra. $2 gtt $3 579870
650 1 4 $a Associative Rings and Algebras. $3 672306
650 2 4 $a Category Theory, Homological Algebra. $3 678397
650 2 4 $a General Algebraic Systems. $3 672227
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319114767
776 0 8 $i Printed edition: $z 9783319114743
856 4 0 $u https://doi.org/10.1007/978-3-319-11475-0
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)